Lesson: Data Sufficiency Challenging - 17t03

Easy Math/Tough Applications: Example 2

A home owner must pick between carpet A, which costs $6.00 per square foot, and carpet B, which costs $4.50 per square foot. If the home owner must pay the installer the same rate regardless of which carpet is used, which of the two carpets will be cheaper to install?

1) Carpet B takes one-third longer to install than carpet A.

2) Labor costs are $20 per hour.

Review the question stem above. What other factor must we take into consideration when determining the total cost of Carpet A and Carpet B? Type your answer into the Text Box and then click Continue.

The total cost depends on the cost of the carpet, area, installation rate, and .

Review Statement 1 below. Is it sufficient or insufficient? Select the correct answer and then click Continue.

1) Carpet B takes one-third longer to install than carpet A.

Sufficient

Insufficient

Countinue

So B’s labor cost will be one-third greater than A’s. This can be incorporated into our equations:

Notice that we’ve replaced L _{B with} in the second equation because we know from Statement (1) that L _B = . This makes comparing the equations easier. But can we tell from these equations whether A will cost more than B to install?

No. Why not? Look at it this way: the difference in purchase price is 1.5(area) and the difference in installation costs is , but which of these two unknowns is greater? If 1.5(area) turns out to be greater than , then A will be more expensive to install. But if is greater than 1.5(area), then B will be the costlier one.

Because we still don’t know either or 1.5(area), this statement is insufficient to give us a definitive answer.

Countinue

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